ANOVA

ANOVA is a statistical method that stands for analysis of variance.  ANOVA was developed by Ronald Fisher in 1918 and is the extension of the T and the Z test.  Before the use of ANOVA, the T-test and Z-test were commonly used.  But the problem with the T-test is that it cannot be applied for more than two groups.  In 1918, Ronald Fisher developed a test called the analysis of variance. This test is also called the Fisher analysis of variance, which is used to do the analysis of variance between and within the groups whenever the groups are more than two.  If you set the Type one error to be .05, and you had several groups, each time you tested a mean against another there would be a .05 probability of having a type one error rate.  This would mean that with six T-tests you would have a 0.30 (.05×6) probability of having a type one error rate.  This is much higher than the desired .05.
ANOVA creates a way to test several null hypothesis at the same time.
The logic behind this procedure has to do with how much variance there is in the population.  It is likely he researcher will not know the actual variance in the population but they can estimate this by sampling and calculating the variance in the sample.  You compare the differences in the samples to see if they are the same or statistically different while still accounting for sampling error.

Uses of ANOVA
These days, researchers are using ANOVA in many ways.  The use of ANOVA depends on the research design.  Commonly, researchers are using ANOVA in three ways: one-way ANOVA, two-way ANOVA and N-way Multivariate ANOVA.
One-Way:
When we compare more than two groups, based on one factor (independent variable), this is called one way ANOVA.  For example, it is used if a manufacturing company wants to compare the productivity of three or more employees based on working hours.  This is called one way ANOVA.
Two-Way:
When a company wants to compare the employee productivity based on two factors (2 independent variables), then it said to be two way (Factorial) ANOVA.  For example, based on the working hours and working conditions, if a company wants to compare employee productivity, it can do that through two way ANOVA.  Two-way ANOVA’s can be used to see the effect of one of the factors after controlling for the other, or it can be used to see the INTERACTION between the two factors.  This is a great way to control for extraneous variables as you are able to add them to the design of the study.
Factorial ANOVA can be balanced or unbalanced.  This is to say, you can have the same number of subjects in each group (balanced) or not (unbalanced).  This can come about, depending on the study, as just a reflection of the population, or an unwanted event such as participants not returning to the study.  Not having equal sizes groups can make it appear that there is an effect when this may not be the case.  There are several procedures a researcher can do in order to solve this problem:

·       Discard cases (undesirable)

·       Conduct a special kind of ANOVA which can deal with the unbalanced design

 By: Lera Gay Bacay